Letters on Astronomy Part 18

The comet whose history is the most interesting, and which both of us have been privileged to see, is Halley's. Just before its latest visit, in 1835, its return was antic.i.p.ated with so much expectation, not only by astronomers, but by all cla.s.ses of the community, that a great and laudable eagerness universally prevailed, to learn the particulars of its history. The best summary of these, which I met with, was given in the Edinburgh Review for April, 1835. I might content myself with barely referring you to that well-written article; but, as you may not have the work at hand, and would, moreover, probably not desire to read the whole article, I will abridge it for your perusal, interspersing some remarks of my own. I have desired to give you, in the course of these Letters, some specimen of the labors of astronomers, and shall probably never be able to find a better one.

It is believed that the first recorded appearance of Halley's comet was that which was supposed to signalize the birth of Mithridates, one hundred and thirty years before the birth of Christ. It is said to have appeared for twenty-four days; its light is said to have surpa.s.sed that of the sun; its magnitude to have extended over a fourth part of the firmament; and it is stated to have occupied, consequently, about four hours in rising and setting. In the year 323, a comet appeared in the sign Virgo. Another, according to the historians of the Lower Empire, appeared in the year 399, seventy-six years after the last, at an interval corresponding to that of Halley's comet. The interval between the birth of Mithridates and the year 323 was four hundred and fifty-three years, which would be equivalent to six periods of seventy-five and a half years. Thus it would seem, that in the interim there were five returns of this comet un.o.bserved, or at least unrecorded. The appearance in the year 399 was attended with extraordinary circ.u.mstances. It was described in the old writers as a "comet of monstrous size and appalling aspect, its tail seeming to reach down to the ground." The next recorded appearance of a comet agreeing with the ascertained period marks the taking of Rome, in the year 550,--an interval of one hundred and fifty-one years, or two periods of seventy-five and a half years having elapsed. One unrecorded return must, therefore, have taken place in the interim. The next appearance of a comet, coinciding with the a.s.signed period, is three hundred and eighty years afterwards; namely, in the year 930,--five revolutions having been completed in the interval. The next appearance is recorded in the year 1005, after an interval of a single period of seventy-five years. Three revolutions would now seem to have pa.s.sed unrecorded, when the comet again makes its appearance in 1230. In this, as well as in former appearances, it is proper to state, that the sole test of ident.i.ty of these cornets with that of Halley is the coincidence of the times, as near as historical records enable us to ascertain, with the epochs at which the comet of Halley might be expected to appear. That such evidence, however, is very imperfect, must be evident, if the frequency of cometary appearances be considered, and if it be remembered, that hitherto we find no recorded observations, which could enable us to trace, even with the rudest degree of approximation, the paths of those comets, the times of whose appearances raise a presumption of their ident.i.ty with that of Halley. We now, however, descend to times in which more satisfactory evidence may be expected.

In the year 1305, a year in which the return of Halley's comet might have been expected, there is recorded a comet of remarkable character: "A comet of terrific dimensions made its appearance about the time of the feast of the Pa.s.sover, which was followed by a Great Plague." Had the terrific appearance of this body alone been recorded, this description might have pa.s.sed without the charge of great exaggeration; but when we find the Great Plague connected with it as a consequence, it is impossible not to conclude, that the comet was seen by its historians through the magnifying medium of the calamity which followed it. Another appearance is recorded in the year 1380, unaccompanied by any other circ.u.mstance than its mere date. This, however, is in strict accordance with the ascertained period of Halley's comet.

We now arrive at the first appearance at which observations were taken, possessing sufficient accuracy to enable subsequent investigators to determine the path of the comet; and this is accordingly the first comet the ident.i.ty of which with the comet of Halley can be said to be conclusively established. In the year 1456, a comet is stated to have appeared "of unheard of magnitude;" it was accompanied by a tail of extraordinary length, which extended over sixty degrees, (a third part of the heavens,) and continued to be seen during the whole month of June. The influence which was attributed to this appearance renders it probable, that in the record there is more or less of exaggeration. It was considered as the celestial indication of the rapid success of Mohammed the Second, who had taken Constantinople, and struck terror into the whole Christian world. Pope Calixtus the Second levelled the thunders of the Church against the enemies of his faith, terrestrial and celestial; and in the same Bull excommunicated the Turks and the comet; and, in order that the memory of this manifestation of his power should be for ever preserved, he ordained that the bells of all the churches should be rung at mid-day,--a custom which is preserved in those countries to our times.

The extraordinary length and brilliancy which was ascribed to the tail, upon this occasion, have led astronomers to investigate the circ.u.mstances under which its brightness and magnitude would be the greatest possible; and upon tracing back the motion of the comet to the year 1456, it has been found that it was then actually in the position, with respect to the earth and sun, most favorable to magnitude and splendor. So far, therefore, the result of astronomical calculation corroborates the records of history.

The next return took place in 1531. Pierre Appian, who first ascertained the fact that the tails of comets are usually turned from the sun, examined this comet with a view to verify his statement, and to ascertain the true direction of its tail. He made, accordingly, numerous observations upon its position, which, although rude, compared with the present standard of accuracy, were still sufficiently exact to enable Halley to identify this comet with that observed by himself.

The next return took place in 1607, when the comet was observed by Kepler. This astronomer first saw it on the evening of the twenty-sixth of September, when it had the appearance of a star of the first magnitude, and, to his vision, was without a tail; but the friends who accompanied him had better sight, and distinguished the tail. Before three o'clock the following morning the tail had become clearly visible, and had acquired great magnitude. Two days afterwards, the comet was observed by Longomonta.n.u.s, a distinguished philosopher of the time. He describes its appearance, to the naked eye, to be like Jupiter, but of a paler and more obscured light; that its tail was of considerable length, of a paler light than that of the head, and more dense than the tails of ordinary comets.

The next appearance, and that which was observed by Halley himself, took place in 1682, a little before the publication of the '_Principia_.' In the interval between 1607 and 1682, practical astronomy had made great advances; instruments of observation had been brought to a state of comparative perfection; numerous observatories had been established, and the management of them had been confided to the most eminent men in Europe. In 1682, the scientific world was therefore prepared to examine the visitor of our system with a degree of care and accuracy before unknown.

In the year 1686, about four years afterwards, Newton published his '_Principia_,' in which he applied to the comet of 1680 the general principles of physical investigation first promulgated in that work. He explained the method of determining, by geometrical construction, the visible portion of the path of a body of this kind, and invited astronomers to apply these principles to the various recorded comets,--to discover whether some among them might not have appeared at different epochs, the future returns of which might consequently be predicted. Such was the effect of the force of a.n.a.logy upon the mind of Newton, that, without awaiting the discovery of a periodic comet, he boldly a.s.sumed these bodies to be a.n.a.logous to planets in their revolution round the sun.

Extraordinary as these conjectures must have appeared at the time, they were soon strictly realized. Halley, who was then a young man, but possessed one of the best minds in England, undertook the labor of examining the circ.u.mstances attending all the comets previously recorded, with a view to discover whether any, and which of them, appeared to follow the same path. Antecedently to the year 1700, four hundred and twenty-five of these bodies had been recorded in history; but those which had appeared before the fourteenth century had not been submitted to any observations by which their paths could be ascertained,--at least, not with a sufficient degree of precision, to afford any hope of identifying them with those of other comets.

Subsequently to the year 1300, however, Halley found twenty-four comets on which observations had been made and recorded, with a degree of precision sufficient to enable him to calculate the actual paths which these bodies followed while they were visible. He examined, with the most elaborate care, the _courses_ of each of these twenty-four bodies; he found the exact points at which each one of them crossed the ecliptic, or their _nodes_; also the angle which the direction of their motion made with that plane,--that is, the _inclination of their orbits_; he also calculated the nearest distance at which each of them approached the sun, or their _perihelion distance_; and the exact place of the body when at that nearest point,--that is, the _longitude of the perihelion_. These particulars are called the _elements_ of a comet, because, when ascertained, they afford sufficient data for determining a comet's path. On comparing these paths, Halley found that one, which had appeared in 1661, followed nearly the same path as one which had appeared in 1532. Supposing, then, these to be two successive appearances of the same comet, it would follow, that its period would be one hundred and twenty-nine years, reckoning from 1661. Had this conjecture been well founded, the comet must have appeared about the year 1790. No comet, however, appeared at or near that time, following a similar path.

In his second conjecture, Halley was more fortunate, as indeed might be expected, since it was formed upon more conclusive grounds. He found that the paths of comets which had appeared in 1531 and 1607 were nearly identical, and that they were in fact the same as the path followed by the comet observed by himself in 1682. He suspected, therefore, that the appearances at these three epochs were produced by three successive returns of the same comet, and that, consequently, its period in its...o...b..t must be about seventy-five and a half years. The probability of this conclusion is strikingly exhibited to the eye, by presenting the elements in a tabular form, from which it will at once be seen how nearly they correspond at these regular intervals.

===================================================================== Time. Inclination of Long. of the Long. Per. Per. Dist. Course.

the orbit. node. ===================================================================== 1456 1756' 4830' 30100' 058' Retrograde.

1531 17 56 49 25 301 39 0 57 "

1607 17 02 50 21 302 16 0 58 "

1682 17 42 50 48 301 36 0 58 "

So little was the scientific world, at this time, prepared for such an announcement, that Halley himself only ventured at first to express his opinion in the form of conjecture; but, after some further investigation of the circ.u.mstances of the recorded comets, he found three which, at least in point of time, agreed with the period a.s.signed to the comet of 1682. Collecting confidence from these circ.u.mstances, he announced his discovery as the result of observation and calculation combined, and ent.i.tled to as much confidence as any other consequence of an established physical law.

There were, nevertheless, two circ.u.mstances which might be supposed to offer some difficulty. First, the intervals between the supposed successive returns were not precisely equal; and, secondly, the inclination of the comet's path to the plane of the earth's...o...b..t was not exactly the same in each case. Halley, however, with a degree of sagacity which, considering the state of knowledge at the time, cannot fail to excite unqualified admiration, observed, that it was natural to suppose that the same causes which disturbed the planetary motions must likewise act upon comets; and that their influence would be so much the more sensible upon these bodies, because of their great distances from the sun. Thus, as the attraction of Jupiter for Saturn was known to affect the velocity of the latter planet, sometimes r.e.t.a.r.ding and sometimes accelerating it, according to their relative position, so as to affect its period to the extent of thirteen days, it might well be supposed, that the comet might suffer by a similar attraction an effect sufficiently great, to account for the inequality observed in the interval between its successive returns: and also for the variation to which the direction of its path upon the plane of the ecliptic was found to be subject. He observed, in fine, that, as in the interval between 1607 and 1682, the comet pa.s.sed so near Jupiter that its velocity must have been augmented, and consequently its period shortened, by the action of that planet, this period, therefore, having been only seventy-five years, he inferred that the following period would probably be seventy-six years, or upwards; and consequently, that the comet ought not to be expected to appear until the end of 1758, or the beginning of 1759. It is impossible to imagine any quality of mind more enviable than that which, in the existing state of mathematical physics, could have led to such a prediction. The imperfect state of mathematical science rendered it impossible for Halley to offer to the world a demonstration of the event which he foretold. The theory of gravitation, which was in its infancy in the time of Halley's investigations, had grown to comparative maturity before the period at which his prediction could be fulfilled. The exigencies of that theory gave birth to new and more powerful instruments of mathematical inquiry: the differential and integral calculus, or the science of fluxions, as it is sometimes called,--a branch of the mathematics, expressed by algebraic symbols, but capable of a much higher reach, as an instrument of investigation, than either algebra or geometry,--was its first and greatest offspring.

This branch of science was cultivated with an ardor and success by which it was enabled to answer all the demands of physics, and it contributed largely to the advancement of mechanical science itself, building upon the laws of motion a structure which has since been denominated 'Celestial Mechanics.' Newton's discoveries having obtained reception throughout the scientific world, his inquiries and his theories were followed up; and the consequences of the great principle of universal gravitation were rapidly developed. Since, according to this doctrine, _every body in nature attracts and is attracted by every other body_, it follows, that the comet was liable to be acted on by each of the planets, as well as by the sun,--a circ.u.mstance which rendered its movements much more difficult to follow, than would be the case were it subject merely to the projectile force and to the solar attraction. To estimate the time it would take for a s.h.i.+p to cross the Atlantic would be an easy task, were she subject to only one constant wind; but to estimate, beforehand, the exact influence which all other winds and the tides might have upon her pa.s.sage, some accelerating and some r.e.t.a.r.ding her course, would present a problem of the greatest difficulty. Clairaut, however, a celebrated French mathematician, undertook to estimate the effects that would be produced on Halley's comet by the attractions of all the planets. His aim was to investigate _general rules_, by which the computation could be made arithmetically, and hand them over to the practical calculator, to make the actual computations. Lalande, a practical astronomer, no less eminent in his own department, and who indeed first urged Clairaut to this inquiry, undertook the management of the astronomical and arithmetical part of the calculation. In this prodigious labor (for it was one of most appalling magnitude) he was a.s.sisted by the wife of an eminent watchmaker in Paris, named Lepaute, whose exertions on this occasion have deservedly registered her name in astronomical history.

It is difficult to convey to one who is not conversant with such investigations, an adequate notion of the labor which such an inquiry involved. The calculation of the influence of any one _planet_ of the system upon any other is itself a problem of some complexity and difficulty; but still, one general computation, depending upon the calculation of the terms of a certain series, is sufficient for its solution. This comparative simplicity arises entirely from two circ.u.mstances which characterize the planetary orbits. These are, that, though they are ellipses, they differ very slightly from circles; and though the planets do not move in the plane of the ecliptic, yet none of them deviate considerably from that plane. But these characters do not belong to the orbits of comets, which, on the contrary, are highly eccentric, and make all possible angles with the ecliptic. The consequence of this is, that the calculation of the disturbances produced in the cometary orbits by the action of the planets must be conducted not like the planets, in one general calculation applicable to the whole orbits, but in a vast number of separate calculations; in which the orbit is considered, as it were, bit by bit, each bit requiring a calculation similar to the whole orbit of the planet. Now, when it is considered that the period of Halley's comet is about seventy-five years, and that every portion of its course, for two successive periods, was necessary to be calculated separately in this way, some notion may be formed of the labor encountered by Lalande and Madame Lepaute. "During six months," says Lalande, "we calculated from morning till night, sometimes even at meals; the consequence of which was, that I contracted an illness which changed my const.i.tution for the remainder of my life. The a.s.sistance rendered by Madame Lepaute was such, that, without her, we never could have dared to undertake this enormous labor, in which it was necessary to calculate the distance of each of the two planets, Jupiter and Saturn, from the comet, and their attraction upon that body, separately, for every successive degree, and for one hundred and fifty years."

The attraction of a body is proportioned to its quant.i.ty of matter.

Therefore, before the attraction exerted upon the comet by the several planets within whose influence it might fall, could be correctly estimated, it was necessary to know the ma.s.s of each planet; and though the planets had severally been weighed by methods supplied by Newton's 'Principia,' yet the estimate had not then attained the same measure of accuracy as it has now reached; nor was it certain that there was not (as it has since appeared that there actually was) one or more planets beyond Saturn, whose attractions might likewise influence the motions of the comet. Clairaut, making the best estimate he was able, under all these disadvantages, of the disturbing influence of the planets, fixed the return of the comet to the place of its nearest distance from the sun on the fourth of April, 1759.

In the successive appearances of the comet, subsequently to 1456, it was found to have gradually decreased in magnitude and splendor. While in 1456 it reached across one third part of the firmament, and spread terror over Europe, in 1607, its appearance, when observed by Kepler and Longomonta.n.u.s, was that of a star of the first magnitude; and so trifling was its tail that, Kepler himself, when he first saw it, doubted whether it had any. In 1682, it excited little attention, except among astronomers. Supposing this decrease of magnitude and brilliancy to be progressive, Lalande entertained serious apprehensions that on its expected return it might be so inconsiderable, as to escape the observation even of astronomers; and thus, that this splendid example of the power of science, and unanswerable proof of the principle of gravitation, would be lost to the world.

It is not uninteresting to observe the misgivings of this distinguished astronomer with respect to the appearance of the body, mixed up with his unshaken faith in the result of the astronomical inquiry. "We cannot doubt," says he, "that it will return; and even if astronomers cannot see it, they will not therefore be the less convinced of its presence.

They know that the faintness of its light, its great distance, and perhaps even bad weather, may keep it from our view. But the world will find it difficult to believe us; they will place this discovery, which has done so much honor to modern philosophy, among the number of chance predictions. We shall see discussions spring up again in colleges, contempt among the ignorant, terror among the people; and seventy-six years will roll away, before there will be another opportunity of removing all doubt."

Fortunately for science, the arrival of the expected visitor did not take place under such untoward circ.u.mstances. As the commencement of the year 1759 approached, "astronomers," says Voltaire, "hardly went to bed at all." The honor, however, of the first glimpse of the stranger was not reserved for the possessors of scientific rank, nor for the members of academies or universities. On the night of Christmas-day, 1758, George Palitzch, of Politz, near Dresden,--"a peasant," says Sir John Herchel, "by station, an astronomer by nature," first saw the comet.

An astronomer of Leipzic found it soon after; but, with the mean jealousy of a miser, he concealed his treasure, while his contemporaries throughout Europe were vainly directing their anxious search after it to other quarters of the heavens. At this time, Delisle, a French astronomer, and his a.s.sistant, Messier, who, from his unweared a.s.siduity in the pursuit of comets, was called the _Comet-Hunter_, had been constantly engaged, for eighteen months, in watching for the return of Halley's comet. Messier pa.s.sed his life in search of comets. It is related of him, that when he was in expectation of discovering a comet, his wife was taken ill and died. While attending on her, being withdrawn from his observatory, another astronomer antic.i.p.ated him in the discovery. Messier was in despair. A friend, visiting him, began to offer some consolation for the recent affliction he had suffered.

Messier, thinking only of the comet, exclaimed, "I had discovered twelve: alas, that I should be robbed of the thirteenth by Montague!"--and his eyes filled with tears. Then, remembering that it was necessary to mourn for his wife, whose remains were still in the house, he exclaimed, "Ah! this poor woman!" (_ah! cette pauvre femme_,) and again wept for his comet. We can easily imagine how eagerly such an enthusiast would watch for Halley's comet; and we could almost wish that it had been his good fortune to be the first to announce its arrival: but, being misled by a chart which directed his attention to the wrong part of the firmament, a whole month elapsed after its discovery by Palitzch, before he enjoyed the delightful spectacle.

The comet arrived at its perihelion on the thirteenth of March, only twenty-three days from the time a.s.signed by Clairaut. It appeared very round, with a brilliant nucleus, well distinguished from the surrounding nebulosity. It had, however, no appearance of a tail. It became lost in the sun, as it approached its perihelion, and emerged again, on the other side of the sun, on the first of April. Its exhibiting an appearance, so inferior to what it presented on some of its previous returns, is partly accounted for by its being seen by the European astronomers under peculiarly disadvantageous circ.u.mstances, being almost always within the twilight, and in the most unfavorable situations. In the southern hemisphere, however, the circ.u.mstances for observing it were more favorable, and there it exhibited a tail varying from ten to forty-seven degrees in length.

In my next Letter I will give you some particulars respecting the late return of Halley's comet.

LETTER XXVI.

COMETS, CONTINUED.

"Incensed with indignation, Satan stood Unterrified, and like a comet burned, That fires the length of Ophiucus huge In the Arctic sky, and from his horrid train Shakes pestilence and war."--_Milton._

AMONG other great results which have marked the history of Halley's comet, it has itself been a criterion of the existing state of the mathematical and astronomical sciences. We have just seen how far the knowledge of the great laws of physical astronomy, and of the higher mathematics, enabled the astronomers of 1682 and 1759, respectively, to deal with this wonderful body; and let us now see what higher advantages were possessed by the astronomers of 1835. During this last interval of seventy-six years, the science of mathematics, in its most profound and refined branches, has made prodigious advances, more especially in its application to the laws of the celestial motions, as exemplified in the 'Mecanique Celeste' of La Place. The methods of investigation have acquired greater simplicity, and have likewise become more general and comprehensive; and mechanical science, in the largest sense of that term, now embraces in its formularies the most complicated motions, and the most minute effects of the mutual influences of the various members of our system. You will probably find it difficult to comprehend, how such hidden facts can be disclosed by formularies, consisting of _a_'s and _b_'s, and _x_'s and _y_'s, and other algebraic symbols; nor will it be easy to give you a clear idea of this subject, without a more extensive acquaintance than you have formed with algebraic investigations; but you can easily understand that even an equation expressed in numbers may be so changed in its form, by adding, subtracting, multiplying and dividing, as to express some new truth at every transformation. Some idea of this may be formed by the simplest example. Take the following: 3+4=7. This equation expresses the fact, that three added to four is equal to seven. By multiplying all the terms by 2, we obtain a new equation, in which 6+8=14. This expresses a new truth; and by varying the form, by similar operations, an indefinite number of separate truths may be elicited from the simple fundamental expression. I will add another ill.u.s.tration, which involves a little more algebra, but not, I think, more than you can understand; or, if it does, you will please pa.s.s over it to the next paragraph. According to a rule of arithmetical progression, _the sum of all the terms is equal to half the sum of the extremes multiplied into the number of terms_.

Calling the sum of the terms _s_, the first term _a_, the last _h_, and the number of terms _n_, and we have _(1/2)n(a+h)=s_; or _n(a+h)=2s_; or _a+h=2s/n_; or _a=(2s/n)-h_; or _h=(2s/n)-a_. These are only a few of the changes which may be made in the original expression, still preserving the equality between the quant.i.ties on the left hand and those on the right; yet each of these transformations expresses a new truth, indicating distinct and (as might be the case) before unknown relations between the several quant.i.ties of which the whole expression is composed. The last, for example, shows us that the last term in an arithmetical series is always equal to twice the sum of the whole series divided by the number of terms and diminished by the first term. In a.n.a.lytical formularies, as expressions of this kind are called, the value of a single unknown quant.i.ty is sometimes given in a very complicated expression, consisting of known quant.i.ties; but before we can ascertain their united value, we must reduce them, by actually performing all the additions, subtractions, multiplications, divisions, raising to powers, and extracting roots, which are denoted by the symbols. This makes the actual calculations derived from such formularies immensely laborious. We have already had an instance of this in the calculations made by Lalande and Madame Lepaute, from formularies furnished by Clairaut.

The a.n.a.lytical formularies, contained in such works as La Place's 'Mecanique Celeste,' exhibit to the eye of the mathematician a record of all the evolutions of the bodies of the solar system in ages past, and of all the changes they must undergo in ages to come. Such has been the result of the combination of transcendent mathematical genius and unexampled labor and perseverance, for the last century. The learned societies established in various centres of civilization have more especially directed their attention to the advancement of physical astronomy, and have stimulated the spirit of inquiry by a succession of prizes, offered for the solutions of problems arising out of the difficulties which were progressively developed by the advancement of astronomical knowledge. Among these questions, the determination of the return of comets, and the disturbances which they experience in their course, by the action of the planets near which they happen to pa.s.s, hold a prominent place. In 1826, the French Inst.i.tute offered a prize for the determination of the exact time of the return of Halley's comet to its perihelion in 1835. M. Pontecoulant aspired to the honor. "After calculations," says he, "of which those alone who have engaged in such researches can estimate the extent and appreciate the fastidious monotony, I arrived at a result which satisfied all the conditions proposed by the Inst.i.tute. I determined the perturbations of Halley's comet, by taking into account the simultaneous actions of Jupiter, Saturn, Ura.n.u.s, and the Earth, and I then fixed its return to its perihelion for the seventh of November." Subsequently to this, however, M. Pontecoulant made some further researches, which led him to correct the former result; and he afterwards altered the time to November fourteenth. It actually came to its perihelion on the sixteenth, within two days of the time a.s.signed.

Nothing can convince us more fully of the complete mastery which astronomers have at last acquired over these erratic bodies, than to read in the Edinburgh Review for April, 1835, the paragraph containing the final results of all the labors and antic.i.p.ations of astronomers, matured as they were, in readiness for the approaching visitant, and then to compare the prediction with the event, as we saw it fulfilled a few months afterwards. The paragraph was as follows: "On the whole, it may be considered as tolerably certain, that the comet will become visible in every part of Europe about the latter end of August, or beginning of September, next. It will most probably be distinguishable by the naked eye, like a star of the first magnitude, but with a duller light than that of a planet, and surrounded with a pale nebulosity, which will slightly impair its splendor. On the night of the seventh of October, the comet will approach the well-known constellation of the Great Bear; and between that and the eleventh, it will pa.s.s directly through the seven conspicuous stars of that constellation, (the Dipper.) Towards the end of November, the comet will plunge among the rays of the sun, and disappear, and will not issue from them, on the other side, until the end of December."

Let us now see how far the actual appearances corresponded to these predictions. The comet was first discovered from the observatory at Rome, on the morning of the fifth of August; by Professor Struve, at Dorpat, on the twentieth; in England and France, on the twenty-third; and at Yale College, by Professor Loomis and myself, on the thirty-first. On the morning of that day, between two and three o'clock, in obedience to the directions which the great minds that had marked out its path among the stars had prescribed, we directed Clarke's telescope (a n.o.ble instrument, belonging to Yale College) towards the northeastern quarter of the heavens, and lo! there was the wanderer so long foretold,--a dim speck of fog on the confines of creation. It came on slowly, from night to night, increasing constantly in magnitude and brightness, but did not become distinctly visible to the naked eye until the twenty-second of September. For a month, therefore, astronomers enjoyed this interesting spectacle before it exhibited itself to the world at large. From this time it moved rapidly along the northern sky, until, about the tenth of October, it traversed the constellation of the Great Bear, pa.s.sing a little above, instead of "through" the seven conspicuous stars const.i.tuting the Dipper. At this time it had a lengthened train, and became, as you doubtless remember, an object of universal interest. Early in November, the comet ran down to the sun, and was lost in his beams; but on the morning of December thirty-first, I again obtained, through Clarke's telescope, a distinct view of it on the other side of the sun, a moment before the morning dawn.

This return of Halley's comet was an astronomical event of transcendent importance. It was the chronicler of ages, and carried us, by a few steps, up to the origin of time. If a gallant s.h.i.+p, which has sailed round the globe, and commanded successively the admiration of many great cities, diverse in language and customs, is invested with a peculiar interest, what interest must attach to one that has made the circuit of the solar system, and fixed the gaze of successive worlds! So intimate, moreover, is the bond which binds together all truths in one indissoluble chain, that the establishment of one great truth often confirms a mult.i.tude of others, equally important. Thus the return of Halley's comet, in exact conformity with the predictions of astronomers, established the truth of all those principles by which those predictions were made. It afforded most triumphant proof of the doctrine of universal gravitation, and of course of the received laws of physical astronomy; it inspired new confidence in the power and accuracy of that instrument (the calculus) by means of which its elements had been investigated; and it proved that the different planets, which exerted upon it severally a disturbing force proportioned to their quant.i.ty of matter, had been correctly weighed, as in a balance.

I must now leave this wonderful body to pursue its sublime march far beyond the confines of Ura.n.u.s, (a distance it has long since reached,) and take a hasty notice of two other comets, whose periodic returns have also been ascertained; namely, those of Biela and Encke.

Biela's comet has a period of six years and three quarters. It has its perihelion near the orbit of the earth, and its aphelion a little beyond that of Jupiter. Its...o...b..t, therefore, is far less eccentric than that of Halley's comet; (see Frontispiece;) it neither approaches so near the sun, nor departs so far from it, as most other known comets: some, indeed, never come nearer to the sun than the orbit of Jupiter, while they recede to an incomprehensible distance beyond the remotest planet.

We might even imagine that they would get beyond the limits of the sun's attraction; nor is this impossible, although, according to La Place, the solar attraction is sensible throughout a sphere whose radius is a hundred millions of times greater than the distance of the earth from the sun, or nearly ten thousand billions of miles.

Some months before the expected return of Biela's comet, in 1832, it was announced by astronomers, who had calculated its path, that it would cross the plane of the earth's...o...b..t very near to the earth's path, so that, should the earth happen at the time to be at that point of her revolution, a collision might take place. This announcement excited so much alarm among the ignorant cla.s.ses in France, that it was deemed expedient by the French academy, that one of their number should prepare and publish an article on the subject, with the express view of allaying popular apprehension. This task was executed by M. Arago. He admitted that the earth would in fact pa.s.s so near the point where the comet crossed the plane of its...o...b..t, that, should they chance to meet there, the earth would be enveloped in the nebulous atmosphere of the comet. He, however, showed that the earth would not be near that point at the same time with the comet, but fifty millions of miles from it.

The comet came at the appointed time, but was so exceedingly faint and small, that it was visible only to the largest telescopes. In one respect, its diminutive size and feeble light enhanced the interest with which it was contemplated; for it was a sublime spectacle to see a body, which, as projected on the celestial vault, even when magnified a thousand times, seemed but a dim speck of fog, still pursuing its way, in obedience to the laws of universal gravitation, with the same regularity as Jupiter and Saturn. We are apt to imagine that a body, consisting of such light materials that it can be compared only to the thinnest fog, would be dissipated and lost in the boundless regions of s.p.a.ce; but so far is this from the truth, that, when subjected to the action of the same forces of projection and solar attraction, it will move through the void regions of s.p.a.ce, and will describe its own orbit about the sun with the same unerring certainty, as the densest bodies of the system.

Encke's comet, by its frequent returns, (once in three and a third years,) affords peculiar facilities for ascertaining the laws of its revolution; and it has kept the appointments made for it with great exactness. On its return in 1839, it exhibited to the telescope a globular ma.s.s of nebulous matter, resembling fog, and moved towards its perihelion with great rapidity. It makes its entire excursions within the orbit of Jupiter.

But what has made Encke's comet particularly famous, is its having first revealed to us the existence of a _resisting medium_ in the planetary s.p.a.ces. It has long been a question, whether the earth and planets revolve in a perfect void, or whether a fluid of extreme rarity may not be diffused through s.p.a.ce. A perfect vacuum was deemed most probable, because no such effects on the motions of the planets could be detected as indicated that they encountered a resisting medium. But a feather, or a lock of cotton, propelled with great velocity, might render obvious the resistance of a medium which would not be perceptible in the motions of a cannon ball. Accordingly, Encke's comet is thought to have plainly suffered a r.e.t.a.r.dation from encountering a resisting medium in the planetary regions. The effect of this resistance, from the first discovery of the comet to the present time, has been to diminish the time of its revolution about two days. Such a resistance, by destroying a part of the projectile force, would cause the comet to approach nearer to the sun, and thus to have its periodic time shortened. The ultimate effect of this cause will be to bring the comet nearer to the sun, at every revolution, until it finally falls into that luminary, although many thousand years will be required to produce this catastrophe. It is conceivable, indeed, that the effects of such a resistance may be counteracted by the attraction of one or more of the planets, near which it may pa.s.s in its successive returns to the sun. Still, it is not probable that this cause will exactly counterbalance the other; so that, if there is such an elastic medium diffused through the planetary regions, it must follow that, in the lapse of ages, every comet will fall into the sun. Newton conjectured that this would be the case, although he did not found his opinion upon the existence of such a resisting medium as is now detected. To such an opinion he adhered to the end of life. At the age of eighty-three, in a conversation with his nephew, he expressed himself thus: "I cannot say when the comet of 1680 will fall into the sun; possibly after five or six revolutions; but whenever that time shall arrive, the heat of the sun will be raised by it to such a point, that our globe will be burned, and all the animals upon it will perish."

Of the _physical nature_ of comets little is understood. The greater part of them are evidently mere ma.s.ses of vapor, since they permit very small stars to be seen through them. In September, 1832, Sir John Herschel, when observing Biela's comet, saw that body pa.s.s directly between his eye and a small cl.u.s.ter of minute telescopic stars of the sixteenth or seventeenth magnitude. This little constellation occupied a s.p.a.ce in the heavens, the breadth of which was not the twentieth part of that of the moon; yet the whole of the cl.u.s.ter was distinctly visible through the comet. "A more striking proof," says Sir John Herschel, "could not have been afforded, of the extreme transparency of the matter of which this comet consists. The most trifling fog would have entirely effaced this group of stars, yet they continued visible through a thickness of the comet which, calculating on its distance and apparent diameter, must have exceeded fifty thousand miles, at least towards its central parts." From this and similar observations, it is inferred, that the nebulous matter of comets is vastly more rare than that of the air we breathe, and hence, that, were more or less of it to be mingled with the earth's atmosphere, it would not be perceived, although it might possibly render the air unwholesome for respiration. M. Arago, however, is of the opinion, that some comets, at least, have a solid nucleus. It is difficult, on any other supposition, to account for the strong light which some of them have exhibited,--a light sufficiently intense to render them visible in the day-time, during the presence of the sun. The intense heat to which comets are subject, in approaching so near the sun as some of them do, is alleged as a sufficient reason for the great expansion of the thin vapory atmospheres which form their tails; and the inconceivable cold to which they are subject, in receding to such a distance from the sun, is supposed to account for the condensation of the same matter until it returns to its original dimensions. Thus the great comet of 1680, at its perihelion, approached within one hundred and forty-six thousand miles of the surface of the sun, a distance of only one sixth part of the sun's diameter. The heat which it must have received was estimated to be equal to twenty-eight thousand times that which the earth receives in the same time, and two thousand times hotter than red-hot iron. This temperature would be sufficient to volatilize the most obdurate substances, and to expand the vapor to vast dimensions; and the opposite effects of the extreme cold to which it would be subject in the regions remote from the sun would be adequate to condense it into its former volume. This explanation, however, does not account for the direction of the tail, extending, as it usually does, only in a line opposite to the sun. Some writers, therefore, suppose that the nebulous matter of the comet, after being expanded to such a volume that the particles are no longer attracted to the nucleus, unless by the slightest conceivable force, are carried off in a direction from the sun, by the impulse of the solar rays themselves. But to a.s.sign such a power to the sun's rays, while they have never been proved to have any momentum, is unphilosophical; and we are compelled to place the phenomena of comets' tails among the points of astronomy yet to be explained.

Since comets which approach very near the sun, like the comet of 1680, cross the orbits of all the planets, the possibility that one of them may strike the earth has frequently been suggested. Still it may quiet our apprehensions on this subject, to reflect on the vast amplitude of the planetary s.p.a.ces, in which these bodies are not crowded together, as we see them erroneously represented in orreries and diagrams, but are spa.r.s.ely scattered at immense distances from each other. They are like insects flying, singly, in the expanse of heaven. If a comet's tail lay with its axis in the plane of the ecliptic when it was near the sun, we can imagine that the tail might sweep over the earth; but the tail may be situated at any angle with the ecliptic, as well as in the same plane with it, and the chances that it will not be in the same plane are almost infinite. It is also extremely improbable that a comet will cross the plane of the ecliptic precisely at the earth's path in that plane, since it may as probably cross it at any other point nearer or more remote from the sun. A French writer of some eminence (Du Sejour) has discussed this subject with ability, and arrived at the following conclusions: That of all the comets whose paths had been ascertained, none _could pa.s.s_ nearer to the earth than about twice the moon's distance; and that none ever _did pa.s.s_ nearer to the earth than nine times the moon's distance. The comet of 1770, already mentioned, which became entangled among the satellites of Jupiter, came within this limit. Some have taken alarm at the idea that a comet, by approaching very near to the earth, might raise so high a _tide_, as to endanger the safety of maritime countries especially: but this writer shows, that the comet could not possibly remain more than two hours so near the earth as a fourth part of the moon's distance; and it could not remain even so long, unless it pa.s.sed the earth under very peculiar circ.u.mstances. For example, if its...o...b..t were nearly perpendicular to that of the earth, it could not remain more than half an hour in such a position. Under such circ.u.mstances, the production of a tide would be impossible. Eleven hours, at least, would be necessary to enable a comet to produce an effect on the waters of the earth, from which the injurious effects so much dreaded would follow. The final conclusion at which he arrives is, that although, in strict geometrical rigor, it is not physically impossible that a comet should encounter the earth, yet the probability of such an event is absolutely nothing.

M. Arago, also, has investigated the probability of such a collision on the mathematical doctrine of chances, and remarks as follows: "Suppose, now, a comet, of which we know nothing but that, at its perihelion, it will be nearer the sun than we are, and that its diameter is equal to one fourth that of the earth; the doctrine of chances shows that, out of two hundred and eighty-one millions of cases, there is but one against us; but one, in which the two bodies could meet."

La Place has a.s.signed the consequences that would result from a direct collision between the earth and a comet. "It is easy," says he, "to represent the effects of the shock produced by the earth's encountering a comet. The axis and the motion of rotation changed; the waters abandoning their former position to precipitate themselves towards the new equator; a great part of men and animals whelmed in a universal deluge, or destroyed by the violent shock imparted to the terrestrial globe; entire species annihilated; all the monuments of human industry overthrown;--such are the disasters which the shock of a comet would necessarily produce." La Place, nevertheless, expresses a decided opinion that the orbits of the planets have never yet been disturbed by the influence of comets. Comets, moreover, have been, and are still to some degree, supposed to exercise much influence in the affairs of this world, affecting the weather, the crops, the public health, and a great variety of atmospheric commotions. Even Halley, finding that his comet must have been near the earth at the time of the Deluge, suggested the possibility that the comet caused that event,--an idea which was taken up by Whiston, and formed into a regular theory. In Gregory's Astronomy, an able work, published at Oxford in 1702, the author remarks, that among all nations and in all ages, it has been observed, that the appearance of a comet has always been followed by great calamities; and he adds, "it does not become philosophers lightly to set down these things as fables." Among the various things ascribed to comets by a late English writer, are hot and cold seasons, tempests, hurricanes, violent hail-storms, great falls of snow, heavy rains, inundations, droughts, famines, thick fogs, flies, gra.s.shoppers, plague, dysentery, contagious diseases among animals, sickness among cats, volcanic eruptions, and meteors, or shooting stars. These notions are too ridiculous to require a distinct refutation; and I will only add, that we have no evidence that comets have hitherto ever exercised the least influence upon the affairs of this world; and we still remain in darkness, with respect to their physical nature, and the purposes for which they were created.